Optimal. Leaf size=192 \[ \frac {\sqrt {2} \left (2 a^2-3 b\right ) \tan ^{-1}\left (\frac {\sqrt {2} \sqrt [4]{a} x \sqrt [4]{a x^4-b x}}{\sqrt {a x^4-b x}-\sqrt {a} x^2}\right )}{3 \sqrt [4]{a} b^2}+\frac {\sqrt {2} \left (2 a^2-3 b\right ) \tanh ^{-1}\left (\frac {\sqrt {a x^4-b x}+\sqrt {a} x^2}{\sqrt {2} \sqrt [4]{a} x \sqrt [4]{a x^4-b x}}\right )}{3 \sqrt [4]{a} b^2}-\frac {4 \left (a x^4-b x\right )^{3/4} \left (b-a x^3\right )}{21 b^2 x^6} \]
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Rubi [B] time = 1.64, antiderivative size = 617, normalized size of antiderivative = 3.21, number of steps used = 20, number of rules used = 14, integrand size = 43, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.326, Rules used = {2056, 6725, 271, 264, 466, 465, 494, 461, 211, 1165, 628, 1162, 617, 204} \begin {gather*} -\frac {\sqrt [4]{x} \left (2 a^2-3 b\right ) \sqrt [4]{a x^3-b} \log \left (\frac {\sqrt {a} x^{3/2}}{\sqrt {a x^3-b}}-\frac {\sqrt {2} \sqrt [4]{a} x^{3/4}}{\sqrt [4]{a x^3-b}}+1\right )}{3 \sqrt {2} \sqrt [4]{a} b^2 \sqrt [4]{a x^4-b x}}+\frac {\sqrt [4]{x} \left (2 a^2-3 b\right ) \sqrt [4]{a x^3-b} \log \left (\frac {\sqrt {a} x^{3/2}}{\sqrt {a x^3-b}}+\frac {\sqrt {2} \sqrt [4]{a} x^{3/4}}{\sqrt [4]{a x^3-b}}+1\right )}{3 \sqrt {2} \sqrt [4]{a} b^2 \sqrt [4]{a x^4-b x}}-\frac {\sqrt {2} \sqrt [4]{x} \left (2 a^2-3 b\right ) \sqrt [4]{a x^3-b} \tan ^{-1}\left (1-\frac {\sqrt {2} \sqrt [4]{a} x^{3/4}}{\sqrt [4]{a x^3-b}}\right )}{3 \sqrt [4]{a} b^2 \sqrt [4]{a x^4-b x}}+\frac {\sqrt {2} \sqrt [4]{x} \left (2 a^2-3 b\right ) \sqrt [4]{a x^3-b} \tan ^{-1}\left (\frac {\sqrt {2} \sqrt [4]{a} x^{3/4}}{\sqrt [4]{a x^3-b}}+1\right )}{3 \sqrt [4]{a} b^2 \sqrt [4]{a x^4-b x}}-\frac {\left (2 a^2-3 b\right ) \left (b-a x^3\right )^2}{21 a^2 b^2 x^5 \sqrt [4]{a x^4-b x}}+\frac {4 a \left (2-\frac {b}{a^2}\right ) \left (b-a x^3\right )}{21 b^2 x^2 \sqrt [4]{a x^4-b x}}-\frac {\left (2 a^2-3 b\right ) \left (b-a x^3\right )}{3 a b^2 x^2 \sqrt [4]{a x^4-b x}}+\frac {\left (2-\frac {b}{a^2}\right ) \left (b-a x^3\right )}{7 b x^5 \sqrt [4]{a x^4-b x}}-\frac {2 \left (b-a x^3\right )}{3 a b x^2 \sqrt [4]{a x^4-b x}} \end {gather*}
Antiderivative was successfully verified.
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Rule 204
Rule 211
Rule 264
Rule 271
Rule 461
Rule 465
Rule 466
Rule 494
Rule 617
Rule 628
Rule 1162
Rule 1165
Rule 2056
Rule 6725
Rubi steps
\begin {align*} \int \frac {b-3 a x^3+3 x^6}{x^6 \left (-b+2 a x^3\right ) \sqrt [4]{-b x+a x^4}} \, dx &=\frac {\left (\sqrt [4]{x} \sqrt [4]{-b+a x^3}\right ) \int \frac {b-3 a x^3+3 x^6}{x^{25/4} \sqrt [4]{-b+a x^3} \left (-b+2 a x^3\right )} \, dx}{\sqrt [4]{-b x+a x^4}}\\ &=\frac {\left (\sqrt [4]{x} \sqrt [4]{-b+a x^3}\right ) \int \left (-\frac {3 \left (2-\frac {b}{a^2}\right )}{4 x^{25/4} \sqrt [4]{-b+a x^3}}+\frac {3}{2 a x^{13/4} \sqrt [4]{-b+a x^3}}+\frac {-2 a^2 b+3 b^2}{4 a^2 x^{25/4} \sqrt [4]{-b+a x^3} \left (-b+2 a x^3\right )}\right ) \, dx}{\sqrt [4]{-b x+a x^4}}\\ &=\frac {\left (3 \sqrt [4]{x} \sqrt [4]{-b+a x^3}\right ) \int \frac {1}{x^{13/4} \sqrt [4]{-b+a x^3}} \, dx}{2 a \sqrt [4]{-b x+a x^4}}-\frac {\left (3 \left (2-\frac {b}{a^2}\right ) \sqrt [4]{x} \sqrt [4]{-b+a x^3}\right ) \int \frac {1}{x^{25/4} \sqrt [4]{-b+a x^3}} \, dx}{4 \sqrt [4]{-b x+a x^4}}+\frac {\left (\left (-2 a^2 b+3 b^2\right ) \sqrt [4]{x} \sqrt [4]{-b+a x^3}\right ) \int \frac {1}{x^{25/4} \sqrt [4]{-b+a x^3} \left (-b+2 a x^3\right )} \, dx}{4 a^2 \sqrt [4]{-b x+a x^4}}\\ &=\frac {\left (2-\frac {b}{a^2}\right ) \left (b-a x^3\right )}{7 b x^5 \sqrt [4]{-b x+a x^4}}-\frac {2 \left (b-a x^3\right )}{3 a b x^2 \sqrt [4]{-b x+a x^4}}-\frac {\left (3 a \left (2-\frac {b}{a^2}\right ) \sqrt [4]{x} \sqrt [4]{-b+a x^3}\right ) \int \frac {1}{x^{13/4} \sqrt [4]{-b+a x^3}} \, dx}{7 b \sqrt [4]{-b x+a x^4}}+\frac {\left (\left (-2 a^2 b+3 b^2\right ) \sqrt [4]{x} \sqrt [4]{-b+a x^3}\right ) \operatorname {Subst}\left (\int \frac {1}{x^{22} \sqrt [4]{-b+a x^{12}} \left (-b+2 a x^{12}\right )} \, dx,x,\sqrt [4]{x}\right )}{a^2 \sqrt [4]{-b x+a x^4}}\\ &=\frac {\left (2-\frac {b}{a^2}\right ) \left (b-a x^3\right )}{7 b x^5 \sqrt [4]{-b x+a x^4}}-\frac {2 \left (b-a x^3\right )}{3 a b x^2 \sqrt [4]{-b x+a x^4}}+\frac {4 a \left (2-\frac {b}{a^2}\right ) \left (b-a x^3\right )}{21 b^2 x^2 \sqrt [4]{-b x+a x^4}}+\frac {\left (\left (-2 a^2 b+3 b^2\right ) \sqrt [4]{x} \sqrt [4]{-b+a x^3}\right ) \operatorname {Subst}\left (\int \frac {1}{x^8 \sqrt [4]{-b+a x^4} \left (-b+2 a x^4\right )} \, dx,x,x^{3/4}\right )}{3 a^2 \sqrt [4]{-b x+a x^4}}\\ &=\frac {\left (2-\frac {b}{a^2}\right ) \left (b-a x^3\right )}{7 b x^5 \sqrt [4]{-b x+a x^4}}-\frac {2 \left (b-a x^3\right )}{3 a b x^2 \sqrt [4]{-b x+a x^4}}+\frac {4 a \left (2-\frac {b}{a^2}\right ) \left (b-a x^3\right )}{21 b^2 x^2 \sqrt [4]{-b x+a x^4}}+\frac {\left (\left (-2 a^2 b+3 b^2\right ) \sqrt [4]{x} \sqrt [4]{-b+a x^3}\right ) \operatorname {Subst}\left (\int \frac {\left (1-a x^4\right )^2}{x^8 \left (-b-a b x^4\right )} \, dx,x,\frac {x^{3/4}}{\sqrt [4]{-b+a x^3}}\right )}{3 a^2 b^2 \sqrt [4]{-b x+a x^4}}\\ &=\frac {\left (2-\frac {b}{a^2}\right ) \left (b-a x^3\right )}{7 b x^5 \sqrt [4]{-b x+a x^4}}-\frac {2 \left (b-a x^3\right )}{3 a b x^2 \sqrt [4]{-b x+a x^4}}+\frac {4 a \left (2-\frac {b}{a^2}\right ) \left (b-a x^3\right )}{21 b^2 x^2 \sqrt [4]{-b x+a x^4}}+\frac {\left (\left (-2 a^2 b+3 b^2\right ) \sqrt [4]{x} \sqrt [4]{-b+a x^3}\right ) \operatorname {Subst}\left (\int \left (-\frac {1}{b x^8}+\frac {3 a}{b x^4}-\frac {4 a^2}{b \left (1+a x^4\right )}\right ) \, dx,x,\frac {x^{3/4}}{\sqrt [4]{-b+a x^3}}\right )}{3 a^2 b^2 \sqrt [4]{-b x+a x^4}}\\ &=\frac {\left (2-\frac {b}{a^2}\right ) \left (b-a x^3\right )}{7 b x^5 \sqrt [4]{-b x+a x^4}}-\frac {\left (2 a^2-3 b\right ) \left (b-a x^3\right )}{3 a b^2 x^2 \sqrt [4]{-b x+a x^4}}-\frac {2 \left (b-a x^3\right )}{3 a b x^2 \sqrt [4]{-b x+a x^4}}+\frac {4 a \left (2-\frac {b}{a^2}\right ) \left (b-a x^3\right )}{21 b^2 x^2 \sqrt [4]{-b x+a x^4}}-\frac {\left (2 a^2-3 b\right ) \left (b-a x^3\right )^2}{21 a^2 b^2 x^5 \sqrt [4]{-b x+a x^4}}-\frac {\left (4 \left (-2 a^2 b+3 b^2\right ) \sqrt [4]{x} \sqrt [4]{-b+a x^3}\right ) \operatorname {Subst}\left (\int \frac {1}{1+a x^4} \, dx,x,\frac {x^{3/4}}{\sqrt [4]{-b+a x^3}}\right )}{3 b^3 \sqrt [4]{-b x+a x^4}}\\ &=\frac {\left (2-\frac {b}{a^2}\right ) \left (b-a x^3\right )}{7 b x^5 \sqrt [4]{-b x+a x^4}}-\frac {\left (2 a^2-3 b\right ) \left (b-a x^3\right )}{3 a b^2 x^2 \sqrt [4]{-b x+a x^4}}-\frac {2 \left (b-a x^3\right )}{3 a b x^2 \sqrt [4]{-b x+a x^4}}+\frac {4 a \left (2-\frac {b}{a^2}\right ) \left (b-a x^3\right )}{21 b^2 x^2 \sqrt [4]{-b x+a x^4}}-\frac {\left (2 a^2-3 b\right ) \left (b-a x^3\right )^2}{21 a^2 b^2 x^5 \sqrt [4]{-b x+a x^4}}-\frac {\left (2 \left (-2 a^2 b+3 b^2\right ) \sqrt [4]{x} \sqrt [4]{-b+a x^3}\right ) \operatorname {Subst}\left (\int \frac {1-\sqrt {a} x^2}{1+a x^4} \, dx,x,\frac {x^{3/4}}{\sqrt [4]{-b+a x^3}}\right )}{3 b^3 \sqrt [4]{-b x+a x^4}}-\frac {\left (2 \left (-2 a^2 b+3 b^2\right ) \sqrt [4]{x} \sqrt [4]{-b+a x^3}\right ) \operatorname {Subst}\left (\int \frac {1+\sqrt {a} x^2}{1+a x^4} \, dx,x,\frac {x^{3/4}}{\sqrt [4]{-b+a x^3}}\right )}{3 b^3 \sqrt [4]{-b x+a x^4}}\\ &=\frac {\left (2-\frac {b}{a^2}\right ) \left (b-a x^3\right )}{7 b x^5 \sqrt [4]{-b x+a x^4}}-\frac {\left (2 a^2-3 b\right ) \left (b-a x^3\right )}{3 a b^2 x^2 \sqrt [4]{-b x+a x^4}}-\frac {2 \left (b-a x^3\right )}{3 a b x^2 \sqrt [4]{-b x+a x^4}}+\frac {4 a \left (2-\frac {b}{a^2}\right ) \left (b-a x^3\right )}{21 b^2 x^2 \sqrt [4]{-b x+a x^4}}-\frac {\left (2 a^2-3 b\right ) \left (b-a x^3\right )^2}{21 a^2 b^2 x^5 \sqrt [4]{-b x+a x^4}}-\frac {\left (\left (-2 a^2 b+3 b^2\right ) \sqrt [4]{x} \sqrt [4]{-b+a x^3}\right ) \operatorname {Subst}\left (\int \frac {1}{\frac {1}{\sqrt {a}}-\frac {\sqrt {2} x}{\sqrt [4]{a}}+x^2} \, dx,x,\frac {x^{3/4}}{\sqrt [4]{-b+a x^3}}\right )}{3 \sqrt {a} b^3 \sqrt [4]{-b x+a x^4}}-\frac {\left (\left (-2 a^2 b+3 b^2\right ) \sqrt [4]{x} \sqrt [4]{-b+a x^3}\right ) \operatorname {Subst}\left (\int \frac {1}{\frac {1}{\sqrt {a}}+\frac {\sqrt {2} x}{\sqrt [4]{a}}+x^2} \, dx,x,\frac {x^{3/4}}{\sqrt [4]{-b+a x^3}}\right )}{3 \sqrt {a} b^3 \sqrt [4]{-b x+a x^4}}+\frac {\left (\left (-2 a^2 b+3 b^2\right ) \sqrt [4]{x} \sqrt [4]{-b+a x^3}\right ) \operatorname {Subst}\left (\int \frac {\frac {\sqrt {2}}{\sqrt [4]{a}}+2 x}{-\frac {1}{\sqrt {a}}-\frac {\sqrt {2} x}{\sqrt [4]{a}}-x^2} \, dx,x,\frac {x^{3/4}}{\sqrt [4]{-b+a x^3}}\right )}{3 \sqrt {2} \sqrt [4]{a} b^3 \sqrt [4]{-b x+a x^4}}+\frac {\left (\left (-2 a^2 b+3 b^2\right ) \sqrt [4]{x} \sqrt [4]{-b+a x^3}\right ) \operatorname {Subst}\left (\int \frac {\frac {\sqrt {2}}{\sqrt [4]{a}}-2 x}{-\frac {1}{\sqrt {a}}+\frac {\sqrt {2} x}{\sqrt [4]{a}}-x^2} \, dx,x,\frac {x^{3/4}}{\sqrt [4]{-b+a x^3}}\right )}{3 \sqrt {2} \sqrt [4]{a} b^3 \sqrt [4]{-b x+a x^4}}\\ &=\frac {\left (2-\frac {b}{a^2}\right ) \left (b-a x^3\right )}{7 b x^5 \sqrt [4]{-b x+a x^4}}-\frac {\left (2 a^2-3 b\right ) \left (b-a x^3\right )}{3 a b^2 x^2 \sqrt [4]{-b x+a x^4}}-\frac {2 \left (b-a x^3\right )}{3 a b x^2 \sqrt [4]{-b x+a x^4}}+\frac {4 a \left (2-\frac {b}{a^2}\right ) \left (b-a x^3\right )}{21 b^2 x^2 \sqrt [4]{-b x+a x^4}}-\frac {\left (2 a^2-3 b\right ) \left (b-a x^3\right )^2}{21 a^2 b^2 x^5 \sqrt [4]{-b x+a x^4}}-\frac {\left (2 a^2-3 b\right ) \sqrt [4]{x} \sqrt [4]{-b+a x^3} \log \left (1+\frac {\sqrt {a} x^{3/2}}{\sqrt {-b+a x^3}}-\frac {\sqrt {2} \sqrt [4]{a} x^{3/4}}{\sqrt [4]{-b+a x^3}}\right )}{3 \sqrt {2} \sqrt [4]{a} b^2 \sqrt [4]{-b x+a x^4}}+\frac {\left (2 a^2-3 b\right ) \sqrt [4]{x} \sqrt [4]{-b+a x^3} \log \left (1+\frac {\sqrt {a} x^{3/2}}{\sqrt {-b+a x^3}}+\frac {\sqrt {2} \sqrt [4]{a} x^{3/4}}{\sqrt [4]{-b+a x^3}}\right )}{3 \sqrt {2} \sqrt [4]{a} b^2 \sqrt [4]{-b x+a x^4}}-\frac {\left (\sqrt {2} \left (-2 a^2 b+3 b^2\right ) \sqrt [4]{x} \sqrt [4]{-b+a x^3}\right ) \operatorname {Subst}\left (\int \frac {1}{-1-x^2} \, dx,x,1-\frac {\sqrt {2} \sqrt [4]{a} x^{3/4}}{\sqrt [4]{-b+a x^3}}\right )}{3 \sqrt [4]{a} b^3 \sqrt [4]{-b x+a x^4}}+\frac {\left (\sqrt {2} \left (-2 a^2 b+3 b^2\right ) \sqrt [4]{x} \sqrt [4]{-b+a x^3}\right ) \operatorname {Subst}\left (\int \frac {1}{-1-x^2} \, dx,x,1+\frac {\sqrt {2} \sqrt [4]{a} x^{3/4}}{\sqrt [4]{-b+a x^3}}\right )}{3 \sqrt [4]{a} b^3 \sqrt [4]{-b x+a x^4}}\\ &=\frac {\left (2-\frac {b}{a^2}\right ) \left (b-a x^3\right )}{7 b x^5 \sqrt [4]{-b x+a x^4}}-\frac {\left (2 a^2-3 b\right ) \left (b-a x^3\right )}{3 a b^2 x^2 \sqrt [4]{-b x+a x^4}}-\frac {2 \left (b-a x^3\right )}{3 a b x^2 \sqrt [4]{-b x+a x^4}}+\frac {4 a \left (2-\frac {b}{a^2}\right ) \left (b-a x^3\right )}{21 b^2 x^2 \sqrt [4]{-b x+a x^4}}-\frac {\left (2 a^2-3 b\right ) \left (b-a x^3\right )^2}{21 a^2 b^2 x^5 \sqrt [4]{-b x+a x^4}}-\frac {\sqrt {2} \left (2 a^2-3 b\right ) \sqrt [4]{x} \sqrt [4]{-b+a x^3} \tan ^{-1}\left (1-\frac {\sqrt {2} \sqrt [4]{a} x^{3/4}}{\sqrt [4]{-b+a x^3}}\right )}{3 \sqrt [4]{a} b^2 \sqrt [4]{-b x+a x^4}}+\frac {\sqrt {2} \left (2 a^2-3 b\right ) \sqrt [4]{x} \sqrt [4]{-b+a x^3} \tan ^{-1}\left (1+\frac {\sqrt {2} \sqrt [4]{a} x^{3/4}}{\sqrt [4]{-b+a x^3}}\right )}{3 \sqrt [4]{a} b^2 \sqrt [4]{-b x+a x^4}}-\frac {\left (2 a^2-3 b\right ) \sqrt [4]{x} \sqrt [4]{-b+a x^3} \log \left (1+\frac {\sqrt {a} x^{3/2}}{\sqrt {-b+a x^3}}-\frac {\sqrt {2} \sqrt [4]{a} x^{3/4}}{\sqrt [4]{-b+a x^3}}\right )}{3 \sqrt {2} \sqrt [4]{a} b^2 \sqrt [4]{-b x+a x^4}}+\frac {\left (2 a^2-3 b\right ) \sqrt [4]{x} \sqrt [4]{-b+a x^3} \log \left (1+\frac {\sqrt {a} x^{3/2}}{\sqrt {-b+a x^3}}+\frac {\sqrt {2} \sqrt [4]{a} x^{3/4}}{\sqrt [4]{-b+a x^3}}\right )}{3 \sqrt {2} \sqrt [4]{a} b^2 \sqrt [4]{-b x+a x^4}}\\ \end {align*}
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Mathematica [C] time = 0.92, size = 244, normalized size = 1.27 \begin {gather*} \frac {\frac {\left (2 a^2-3 b\right ) \left (-16 a x^3 \left (b-2 a x^3\right )^2 \, _3F_2\left (\frac {5}{4},2,2;1,\frac {9}{4};\frac {a x^3}{b-a x^3}\right )+8 a x^3 \left (-24 a^2 x^6+10 a b x^3+b^2\right ) \, _2F_1\left (\frac {5}{4},2;\frac {9}{4};\frac {a x^3}{b-a x^3}\right )+5 \left (128 a^3 x^9-144 a^2 b x^6+13 a b^2 x^3+3 b^3\right ) \, _2F_1\left (\frac {1}{4},1;\frac {5}{4};\frac {a x^3}{b-a x^3}\right )\right )}{a^2 \left (a x^3-b\right )}+15 \left (2-\frac {b}{a^2}\right ) \left (b-a x^3\right ) \left (4 a x^3+3 b\right )+\frac {210 b x^3 \left (a x^3-b\right )}{a}}{315 b^2 x^5 \sqrt [4]{a x^4-b x}} \end {gather*}
Warning: Unable to verify antiderivative.
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IntegrateAlgebraic [A] time = 1.09, size = 192, normalized size = 1.00 \begin {gather*} \frac {\sqrt {2} \left (2 a^2-3 b\right ) \tan ^{-1}\left (\frac {\sqrt {2} \sqrt [4]{a} x \sqrt [4]{a x^4-b x}}{\sqrt {a x^4-b x}-\sqrt {a} x^2}\right )}{3 \sqrt [4]{a} b^2}+\frac {\sqrt {2} \left (2 a^2-3 b\right ) \tanh ^{-1}\left (\frac {\sqrt {a x^4-b x}+\sqrt {a} x^2}{\sqrt {2} \sqrt [4]{a} x \sqrt [4]{a x^4-b x}}\right )}{3 \sqrt [4]{a} b^2}-\frac {4 \left (a x^4-b x\right )^{3/4} \left (b-a x^3\right )}{21 b^2 x^6} \end {gather*}
Antiderivative was successfully verified.
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fricas [F(-1)] time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \text {Timed out} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.51, size = 237, normalized size = 1.23 \begin {gather*} \frac {4 \, {\left (a - \frac {b}{x^{3}}\right )}^{\frac {7}{4}}}{21 \, b^{2}} + \frac {\sqrt {2} {\left (2 \, a^{\frac {11}{4}} - 3 \, a^{\frac {3}{4}} b\right )} \log \left (\sqrt {2} {\left (a - \frac {b}{x^{3}}\right )}^{\frac {1}{4}} a^{\frac {1}{4}} + \sqrt {a - \frac {b}{x^{3}}} + \sqrt {a}\right )}{6 \, a b^{2}} - \frac {\sqrt {2} {\left (2 \, a^{\frac {11}{4}} - 3 \, a^{\frac {3}{4}} b\right )} \log \left (-\sqrt {2} {\left (a - \frac {b}{x^{3}}\right )}^{\frac {1}{4}} a^{\frac {1}{4}} + \sqrt {a - \frac {b}{x^{3}}} + \sqrt {a}\right )}{6 \, a b^{2}} - \frac {{\left (2 \, \sqrt {2} a^{\frac {11}{4}} - 3 \, \sqrt {2} a^{\frac {3}{4}} b\right )} \arctan \left (\frac {\sqrt {2} {\left (\sqrt {2} a^{\frac {1}{4}} + 2 \, {\left (a - \frac {b}{x^{3}}\right )}^{\frac {1}{4}}\right )}}{2 \, a^{\frac {1}{4}}}\right )}{3 \, a b^{2}} - \frac {{\left (2 \, \sqrt {2} a^{\frac {11}{4}} - 3 \, \sqrt {2} a^{\frac {3}{4}} b\right )} \arctan \left (-\frac {\sqrt {2} {\left (\sqrt {2} a^{\frac {1}{4}} - 2 \, {\left (a - \frac {b}{x^{3}}\right )}^{\frac {1}{4}}\right )}}{2 \, a^{\frac {1}{4}}}\right )}{3 \, a b^{2}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [F] time = 0.45, size = 0, normalized size = 0.00 \begin {gather*} \int \frac {3 x^{6}-3 a \,x^{3}+b}{x^{6} \left (2 a \,x^{3}-b \right ) \left (a \,x^{4}-b x \right )^{\frac {1}{4}}}\, dx \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maxima [F] time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \int \frac {3 \, x^{6} - 3 \, a x^{3} + b}{{\left (a x^{4} - b x\right )}^{\frac {1}{4}} {\left (2 \, a x^{3} - b\right )} x^{6}}\,{d x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [F] time = 0.00, size = -1, normalized size = -0.01 \begin {gather*} -\int \frac {3\,x^6-3\,a\,x^3+b}{x^6\,{\left (a\,x^4-b\,x\right )}^{1/4}\,\left (b-2\,a\,x^3\right )} \,d x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [F] time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \int \frac {- 3 a x^{3} + b + 3 x^{6}}{x^{6} \sqrt [4]{x \left (a x^{3} - b\right )} \left (2 a x^{3} - b\right )}\, dx \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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